We
do not know the exact date in January
of Bombelli's birth, but we are certain that historians credit him with
being the first to be brave enough to propose the existence of
imaginary numbers and write their rules. We choose to honor him
on January 4, as "4" is the only integral root of his historic cubic
equation.

Bombelli
knew the three real roots were

but if he used only
Cardan-Tartaglia, the "state-of-the-art" formula for his time, he would
have to
convert

to real numbers. Thus,
the square root of a negative number could produce three perfectly good
solutions.